Research

Articles

- Ramsey's theorem and products in the Weihrauch degrees.

With D. R. Hirschfeldt, Jun Le Goh, Ludovic Patey, and Arno Pauly. Submitted. - Effectiveness for the dual Ramsey theorem.

With S. Flood, R. Solomon, and L. B. Westrick.

Submitted. - Joins in the strong Weihrauch degrees.

Submitted. - A note on the reverse mathematics of the sorites.

Submitted. - The reverse mathematics of Hindman's theorem for sums of exactly two elements.

With B. F. Csima, D. R. Hirschfeldt, C. G. Jockusch, Jr., R. Solomon, and L. B. Westrick.

*Computability*, to appear - The complexity of primes in computable UFDs.

With J. R. Mileti.

*Notre Dame Journal of Formal Logic*, vol. 59, no. 2, pp. 139–156, 2018. - Coloring trees in reverse mathematics.

With L. Patey.

*Advances in Mathematics*, vol. 318, pp. 497–514, 2017. - Effectiveness of Hindman's theorem for bounded sums.

With C. G. Jockusch, Jr., R. Solomon, and L. B. Westrick.

In A. Day, M. Fellows, N. Greenberg, B. Khoussainov, and A. Melnikov (editors),*Proceedings of the International Symposium on Computability and Complexity (in honour of Rod Downey's 60th birthday)*, Lecture Notes in Computer Science, Springer, pp. Springer-Verlag, 134–142, 2017. - The uniform content of partial and linear orders.

With E. P. Astor, R. Solomon, and J. Suggs.

*Annals of Pure and Applied Logic*, vol. 168, no. 6, pp. 1153–1171, 2017. - Notions of robust information coding.

With G. Igusa.

*Computability*, vol. 6, no. 2, pp. 105–124, 2017. - Ramsey's theorem for singletons and strong computable reducibility.

With L. Patey, R. Solomon, and L. B. Westrick.

*Proceedings of the American Mathematical Society*, vol. 145, no. 3, pp. 1343–1355, 2017. - Strong reductions between combinatorial principles.

*Journal of Symbolic Logic*, vol. 81, no. 4, 1405–1431, 2016. - Generics for Mathias forcing over general Turing ideals.

With P. A. Cholak and M. I. Soskova.

*Israel Journal of Mathematics*, vol. 216, no. 2, 583–604, 2016. - On uniform relationships between combinatorial problems.

With F. G. Dorais, J. L. Hirst, J. R. Mileti, and P. Shafer.

*Transactions of the American Mathematical Society*, vol. 368, no. 2, 1321–1359, 2016. - Cohesive avoidance and strong reductions.

*Proceedings of the American Mathematical Society*, vol. 143, no. 2, 869–876, 2015. - Genericity for computable Mathias forcing.

With P. A. Cholak, J. L. Hirst, and T. A. Slaman.

*Annals of Pure and Applied Logic*, vol. 165, no. 9 (Special Issue: CiE 2012), 1418–1428, 2014. - Limits to joining with generics and randoms.

With A. R. Day.

In R. Downey, J. Brendle, R. Goldblatt, and B. Kim (editors)*Proceedings of the 12th Asian Logic Conference*, World Scientific, 76–88, 2013. - On the strength of the finite intersection principle.

With C. Mummert.

*Israel Journal of Mathematics*, vol. 196, no. 1, 345–361, 2013. - Computably enumerable partial orders.

With P. A. Cholak, N. Schweber, and R. A. Shore.

*Computability*, vol. 1, no. 2, 99–107, 2012. - Reverse mathematics and properties of finite character.

With C. Mummert.

*Annals of Pure and Applied Logic*, vol. 163, no. 9, 1243–1251, 2012. - Equivalence of two ways of computing distances from dissimilarities for arbitrary sets of stimuli.

With E. N. Dzhafarov.

*Journal of Mathematical Psychology*, vol. 55, no. 6, 469–472, 2011. - Infinite saturated orders.

*Order*, vol. 28, no. 2, 163–172, 2011. - Stable Ramsey's theorem and measure.

*Notre Dame Journal of Formal Logic*, vol. 52, no. 1, 95–112, 2011. - Pi^0_1 classes, Peano arithmetic, randomness, and computable domination.

With D. E. Diamondstone and R. I. Soare.

*Notre Dame Journal of Formal Logic*, vol. 51, no. 1 (50th Anniversary Issue), 127–159, 2010. - Ramsey's theorem for trees: the polarized tree theorem and notions of stability.

With T. J. Lakins and J. L. Hirst.

*Archive for Mathematical Logic*, vol. 49, no. 3, 399–415, 2010. - Sorites without vagueness II: Comparative sorites.

With E. N. Dzhafarov.

*Theoria*, vol. 76, no. 1, 25–53, 2010. - Sorites without vagueness I: Classificatory sorites.

With E. N. Dzhafarov.

*Theoria*, vol. 76, no. 1, 4–24, 2010. - Ramsey's theorem and cone avoidance.

With C. G. Jockusch, Jr.

*Journal of Symbolic Logic*, vol. 74, no. 2, 557–578, 2009. - The polarized Ramsey's theorem.

With J. L. Hirst.

*Archive for Mathematical Logic*, vol. 48, no. 2, 141–157, 2009. - Definitions of finiteness based on order properties.

With O. De la Cruz and E. J. Hall.

*Fundamenta Mathematicae*, vol. 189, no. 2, 155–172, 2006.

Preliminary reports

- On Mathias generic sets.

With P. A. Cholak and J. L. Hirst.

In S. B. Cooper, A. Dawar, and B. Löwe (editors),*How the world computes: Turing centenary conference and 8th conference on computability in Europe CiE 2012 Cambridge, UK, June 18–23, 2012 proceedings*, Lecture Notes in Computer Science, vol. 7318, Springer, 129–138, 2012.

Reviews

- Review of Robert I. Soare,
*Turing Computability*, Theory and Applications of Computability, Springer-Verlag, Berlin Heidelberg, 2016.

*Bulletin of Symbolic Logic*, vol. 23, no. 1, 113–115, 2017. - Review of Dov M. Gabbay, Akihiro Kanamori, and John Woods (editors),
*Handbook of the History of Logic*, Volume 6: Sets and Extensions in the Twentieth Century, North-Holland, Amsterdam, 2012.

*MAA Reviews*, January 15, 2013.

Book and book chapters

*Reverse Mathematics.*

With C. Mummert.

Theory and Applications of Computability, Springer, in preparation.- Classificatory sorites, probabilistic supervenience, and rule-making.

With E. N. Dzhafarov.

In A. Abasnezhad and O. Bueno (editors),*On the Sorites Paradox*, Springer, to appear. - The sorites paradox: a behavioral approach.

With E. N. Dzhafarov.

In L. Rudolph (editor),*Qualitative Mathematics for the Social Sciences, Mathematical Models for Research on Cultural Dynamics*, Routledge, 105–136, 2012.

Unpublished work

- Reverse mathematics of combinatorial principles.

Thesis, University of Chicago, 2011. - An infinitude of finitudes.

2005.

The Reverse Mathematics Zoo

- RM Zoo, v. 5.0.

The RM Zoo is a program to help organize relations among various reverse mathematical principles, particularly those that fail to be equivalent to any of the big five subsystems of second-order arithmetic. Its goal is to make it easier to see known results and open questions, and thus hopefully to serve as a useful tool to researchers in the field.